Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction
Department of Liberal Arts, Gyeongnam National University of Science and Technology, Jinju-Si 600-758, Gyeongsangnam-do, Korea
Symmetry 2019, 11(12), 1502; https://doi.org/10.3390/sym11121502
Received: 11 November 2019 / Revised: 4 December 2019 / Accepted: 9 December 2019 / Published: 11 December 2019
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality.
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Keywords:
extragradient method; variational inequality; fixed point; pseudocontractions; sequentially weak continuity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Cho, S.Y. Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction. Symmetry 2019, 11, 1502. https://doi.org/10.3390/sym11121502
AMA Style
Cho SY. Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction. Symmetry. 2019; 11(12):1502. https://doi.org/10.3390/sym11121502
Chicago/Turabian StyleCho, Sun Y. 2019. "Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction" Symmetry 11, no. 12: 1502. https://doi.org/10.3390/sym11121502
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